Method and apparatus for calibrating a tunable microlens

ABSTRACT

A tunable microlens uses at least two layers of electrodes and a droplet of conducting liquid. Such a droplet, which forms the optics of the microlens, moves toward an electrode with a higher voltage relative to other electrodes in the microlens. When calibration of the microlens is desired, an equal and constant voltage is passed over the first layer of electrodes and a different, constant voltage is passed over the second layer of electrodes, which may, for example, be disposed in a star-like pattern. A driving force relative to each electrode in the second layer results and is proportional to the length of the circumference of the droplet that intersects with each of the electrodes. This driving force reaches equilbrium, and hence the droplet reaches its nominal centered position relative to the second layer of electrodes, when the length of intersection of the circumference of the droplet with each of the electrodes in the second layer is equal.

FIELD OF THE INVENTION

The present invention relates to microlenses, and more particularly, toliquid microlenses.

BACKGROUND OF THE INVENTION

Lasers, photodetectors, and other optical components are widely used inmany optoelectronic applications such as, for example, opticalcommunications systems. Traditionally in such applications, manualpositioning and tuning of the components is required to maintain thedesired optical coupling between the system components. However, suchmanual positioning can be slow and quite expensive.

More recently, in attempts to eliminate this manual positioning of thesystem components, small tunable lenses (also known as tunablemicrolenses) were developed to achieve optimal optical coupling.Typically, these microlenses are placed between an optical signaltransmitter, such as a laser, and an optical signal receiver, such as aphotodetector. The microlens, which uses a droplet of liquid as a lens,acts to focus the optical signal (e.g., that is emitted by the laser)onto its intended destination (e.g., the photodetector). In some casesthe position and curvature of these microlenses is automatically variedin order to change the optical properties (e.g., the focal length andfocal spot position) of the microlens when, for example, the directionor divergence of a light beam incident upon the microlens varies fromits optimized direction or divergence. Thus, the desired opticalcoupling is maintained between the components of the optical system.Therefore, the manual positioning and adjustment required in previoussystems is either substantially reduced or even completely eliminated.

While the prior art electrowetting-based microlenses described above areuseful in certain applications, they are also limited in certain aspectsof their usefulness. In particular, none of the prior art electrowettingmicrolenses provided a mechanism for achieving automatic microlenscalibration, i.e. its automatic return to some nominal, calibrated statewith a defined position and focal length. This might be disadvantageousin certain applications. For example, there are many situations wheresome sort of a search and optimization algorithm needs to be employed inorder to achieve optimal tuning/positioning of the droplet. In the priorart solutions, which do not use a calibration mechanism to firstcalibrate the position of the droplet, the algorithm must start from anunknown microlens position. This could result in a substantial increasein the time necessary to complete the microlens tuning/positioningprocess.

SUMMARY OF THE INVENTION

While prior microlens embodiments reduce the need for manual positioningor tuning of components of an optical system, we have recognized thatthere remains a need to provide a tunable liquid microlens that iscapable of automatic calibration. In particular, in certain applicationsit may be advantageous to have a microlens that is self-calibrating.Such a microlens would eliminate the time and effort associated withcalibrating a microlens by first moving the droplet to a known positionand then moving the droplet of liquid of the microlens to a nominal,calibrated position.

Therefore, we have invented a microlens that uses at least two layers ofelectrodes, one of which acts as a layer of calibrating electrodes. Whena calibrating voltage is applied to the electrodes in this calibratinglayer, the droplet, which forms the optics of the microlens, willquickly and automatically reach a nominal, calibrated position relativeto the calibration electrodes in the microlens.

One embodiment of such a self-tunable microlens comprises a transparentconducting substrate of a material (such as transparent ITO (indium tinoxide) glass) that is transparent to at least one wavelength of lightuseful in an optical system. A first, lower layer of electrodes isdisposed within a dielectric material which is in turn disposed on thetransparent conducting substrate. Each of these electrodes is attachedto at least one voltage source so that the electrodes in the first,lower layer may be selectively biased to create a respective voltagepotential between a droplet of conducting liquid disposed on thedielectric material and each of the electrodes in the first, lowerlayer. The droplet of liquid tends to move to a higher voltage and,therefore, can be repositioned by varying the voltages applied to thisfirst, lower layer of electrodes. The layer of dielectric insulatingmaterial separates the first, lower layer of electrodes from the dropletof conducting liquid and the transparent conducting substrate.

A second, upper layer of electrodes is disposed within the dielectricinsulating layer between the first, lower layer of electrodes and thedroplet. When calibration of the lens is required (e.g., aftercommunications have concluded, or when the system of which the microlensis a part is reset for any reason), a constant and equal voltage isapplied to the electrodes in the second, upper layer in such a way thatthe droplet of conducting liquid is adjusted to its nominal, calibratedposition relative to the electrodes in the second, upper layer.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows a prior art microlens and its operational effect on a beamof light.

FIG. 2 shows a prior art microlens wherein a voltage differentialbetween an electrode and a droplet of conducting liquid is used toadjust the focal length of the lens.

FIGS. 3A and 3B show a prior art microlens wherein the droplet ofconducting liquid is electrically coupled to a substrate via a well.

FIG. 4 shows the prior art microlens of FIGS. 3A and 3B wherein avoltage selectively applied to one or more electrodes results in amovement of the droplet away from its centered position relative to theelectrodes.

FIG. 5 shows a microlens in accordance with the present inventionwherein a second, upper layer of electrodes is used to automaticallycalibrate the droplet of conducting liquid.

FIG. 6 shows a top plan view of the microlens of FIG. 5 wherein thedroplet of conducting liquid is automatically calibrated in response toa voltage differential between the second, upper layer of electrodes andthe droplet.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a prior art embodiment of a liquid microlens 101 includinga small droplet 102 of a transparent liquid, such as water, typically(but not necessarily) with a diameter from several micrometers toseveral millimeters. The droplet is disposed on a transparent substrate103 which is typically hydrophobic or includes a hydrophobic coating.The droplet 102 and substrate 103 need only be transparent to lightwaves having a wavelength within a selected range. Light waves 104 passthrough the liquid microlens focal point/focal spot 105 in a focal plane106 that is a focal distance “f” from the contact plane 107 between thedroplet 102 and the substrate 103.

The contact angle θ between the droplet and the substrate is determinedby interfacial surface tensions (also known as interfacial energy) “γ”,generally measured in milli-Newtons per meter (mN/m). As used herein,γ_(S-V) is the interfacial tenson between the substrate 103 and the air,gas or other liquid that surrounds the substrate, γ_(L-V) is theinterfacial tension between the droplet 102 and the air, gas or otherliquid that surrounds the droplet, and γ_(S-L) is the interfacialtension between the substrate 103 and the droplet 102. The contact angleθ may be determined from equation (1):cos θ=(Y _(S-V) −γ _(S-L))/γ_(L-V)  Equation (1)The radius “R” in meters of the surface curvature of the droplet isdetermined by the contact angle θ and the droplet volume in cubic meters(m³) according to equation (2) as follows:R ³=3*(Volume)/[π*(1−cos θ)(2−cos² θ−cos θ)]  Equation (2)The focal length in meters is a function of the radius and therefractive indices “n”, where n_(Liquid) is the refractive index of thedroplet and n_(Vapor) is the refractive index of the air, gas or otherliquid that surrounds the droplet 102. The focal length f may bedetermined from Equation (3):f=R/(n _(Liquid) −n _(Vapor))  Equation (3)The refractive index of the substrate 103 is not critical because of theparallel entry and exit planes of the light waves. The focal length ofthe microlens 101, therefore, is a function of the contact angle θ.

FIG. 2 shows a prior art microlens 201 whereby the phenomenon ofelectrowetting may be used to reversibly change the contact angle θbetween a droplet 202 of a conducting liquid (which may or may not betransparent) and a dielectric insulating layer 203 having a thickness“d” and a dielectric constant ε_(r). An electrode 204, such as metalelectrode is positioned below the dielectric layer 203 and is insulatedfrom the droplet 202 by that layer. The droplet 202 may be, for example,a water droplet, and the dielectric insulating layer 203 may be, forexample, a Teflon/Parylene surface.

When no voltage difference is present between the droplet 202 and theelectrode 204, the droplet 202 maintains its shape defined by the volumeof the droplet and contact angle θ₁, where θ₁ is determined by theinterfacial tensions γ as explained above. When a voltage V is appliedto the electrode 204, the voltage difference between the electrode 204and the droplet 202 causes the droplet to spread. The dashed line 205illustrates that the droplet 202 spreads equally across the layer 203from its central position relative to the electrode 204. Specifically,the contact angle θ decreases from θ₁ to θ₂ when the voltage is appliedbetween the electrode 204 and the droplet 202. The voltage V necessaryto achieve this spreading may range from several volts to severalhundred volts. The amount of spreading, i.e., as determined by thedifference between θ₁ and θ₂, is a function of the applied voltage V.The contact angle θ₂ can be determined from equation (4):cos θ(V)=cos θ(V=0)+V ²(ε₀ε_(r))/(3dγ _(L-V))  Equation (4)where cos θ (V=0) is the contact angle between the insulating layer 203and the droplet 202 when no voltage is applied between the droplet 202and electrode 204; γ_(L-V) is the droplet interfacial tension describedabove; ε_(r) is the dielectric constant of the insulating layer 203; andε₀ is 8.85×10⁻¹² F/M—the permittivity of a vacuum.

FIGS. 3A and 3B illustrate a prior art tunable liquid microlens 301 thatis capable of varying both position and focal length. Referring to FIG.3A, a tunable liquid microlens 301 includes a droplet 302 of atransparent conductive liquid disposed on a first surface of atransparent, dielectric insulating layer 303. The microlens 301 includesa plurality of electrodes 305 insulated from the droplet 302 by theinsulating layer 303. A conducting transparent substrate 304 supportsthe electrodes 305 and the insulating layer 303 and is connected to thedroplet 302 via a well 306 running through the dielectric insulatinglayer 303. Thus, when voltage V_(O) is passed over the conductingtransparent substrate 304, the droplet 302 also experiences voltageV_(O).

FIG. 3B is a top plan view of an illustrative configuration for theelectrodes 305. Each electrode is coupled to a respective voltage V₁through V₄ and the droplet 302, which is centered initially relative tothe electrodes, is coupled to a voltage V_(O) via the well 306. Whenthere is no voltage difference between the droplet 302 and any of theelectrodes 305 (i.e., V₁=V₂=V₃=V₄=V_(O)), and the droplet 302 iscentered relative to the electrodes and quadrants I thru IV, the droplet302 assumes a shape as determined by contact angle θ₁ and the volume ofdroplet 302 in accordance with equations (1)-(3) expained above. Theposition of the droplet 302 and the focal length of the microlens can beadjusted by selectively applying a voltage potential between the droplet302 and the electrodes 305. If equal voltages are applied to all fourelectrodes (i.e., V₁=V₂=V₃=V₄:V_(O)), then the droplet 302 spreadsequally within quadrants I, II, III and IV (i.e., equally along lateralaxes X and Y). Thus, the contact angle θ between the droplet 302 andinsulating layer 303 decreases from θ₂ to θ₁ in FIG. 3A. The resultingshape of the droplet 302 is shown as the dashed line 307 in FIG. 3A.This new shape of the droplet 302 with contact angle θ₁ increases thefocal length of the microlens 301 from the focal length of the microlenswith the initial contact angle θ₂ (i.e., when V₁=V₂=V₃=V₄=V_(O)).

FIG. 4 shows the prior art microlens of FIG. 3A and FIG. 3B wherein thelateral positioning of the droplet, 301 in FIGS. 3A and 3B, along the Xand Y axes can also be changed relative to the initial location of thedroplet by selectively applying voltages to one or more of theelectrodes, 305 in FIGS. 3A and 3B. For example, referring to FIG. 4, bymaking V₁=V₃=V_(O) and by making V₂ greater than V₄, the droplet 402 isattracted toward the higher voltage of the electrode 404 and thus movesin direction 407 toward quadrant II. As discussed above, by adjustingthe lateral position of the droplet 402, the lateral position of thefocal spot of the microlens 401 in that microlens' focal plane is alsoadjusted. Thus, by selectively adjusting the voltage applied to one ormore of the electrodes 403, 404, 405 and 406 relative to the droplet 402in different combinations, the focal length and the lateral position ofthe microlens 401 can be selectively adjusted.

While the prior art electrowetting-based microlens embodiments describedabove are useful in certain applications, they are also limited incertain aspects of their usefulness. In particular, none of the priorart electrowetting microlenses provided a mechanism for achievingautomatic microlens calibration, i.e. its automatic return to somenominal, calibrated state with a defined position and focal length. Thismight be disadvantageous in certain applications. For example, there aremany situations where some sort of a search and optimization algorithmneeds to be employed in order to achieve optimal tuning/positioning ofthe droplet. The prior art solutions, not using a calibration mechanismto first calibrate the position of the droplet, require this algorithmto start from a new and unknown microlens position. This could result ina substantial increase in the time necessary to complete the microlenstuning/positioning process. Additionally, an automatic calibrationability would permit the microlens to reset itself to a nominal,well-defined position that is advantageous for initiating operations orfor testing purposes. Thus, there remains a need to provide a tunableliquid microlens that is capable of automatic calibration.

FIG. 5 shows a first embodiment of the present invention wherein aself-calibrating liquid microlens 501 includes a droplet 502 of atransparent conductive liquid disposed on a first surface of ahydrophobic layer 503 which is in turn disposed on a dielectricinsulating layer 504. Illustrative dielectric insulating materialsinclude the aforementioned Teflon/Parylene surface. Alternatively, thedielectric insulating layer 504 could be made of a hydrophobic material,thus eliminating the need for a separate hydrophobic layer 503. Themicrolens 501 includes a first, lower layer of electrodes 505 (shown incross section in FIG. 5 as electrodes 505 a and 505 b), and a second,upper layer of electrodes 515 (shown in cross section in FIG. 5 aselectrodes 515 a and 515 b. The electrodes 505 and 515 are insulatedfrom the droplet 502 by the dielectric insulating layer 504. Aconducting transparent substrate 506, such as a substrate made from ITO(indium tin oxide) glass, supports the electrodes 505 and the insulatinglayer 504, and is connected to the droplet 502 via a well 512 runningthrough the hydrophobic layer 503 and the dielectric insulating layer504. A voltage V_(O) is applied to the conducting transparent substrate506 and, hence, the droplet 502. The droplet 502 may advantageously beenclosed in an enclosure liquid or gas 509.

Operations of the microlens are initiated with the droplet in a nominallocation, for example centered on the surface 503 relative to theelectrodes 505. Voltage V_(c) over electrodes 515 is, for example,initally set to 0 volts. A constant voltage, not necessarily equal tovoltage V_(c), is also passed initially passed over electrodes 505 suchthat all electrodes in that layer experience the same voltage (e.g., inFIG. 5, V₁=V₅). When a light beam 511 of a selected wavelength, such asthat generated by a laser, is aligned with the microlens 501, theelectronic circuit 507 maintains the constant voltage V₁=V₅ across allelectrodes in layer 505 via leads 506.

When the light beam becomes misaligned with the microlens for anyreason, the electronic circuit will adjust the voltages across theelectrodes in layer 505 such that the droplet 502 will move and becomere-aligned with light beam 511. Various methods and apparatus which maybe used to detect misalignment and to accomplish this realignmentfunction are described in the copending U.S. patent application Ser. No.09/884,605, filed Jun. 19, 2001, entitled “Tunable Liquid Microlens;”Ser. No. 09/951,637, filed Sep. 13, 2001, entitled “Tunable LiquidMicrolens With Lubrication Assisted Electrowetting;” and Ser. No.______, filed Apr. 30, 2002, entitled “Method and Apparatus for Aligninga Photo-Tunable Microlens.” In all of the techniques described in theseapplications, the microlens is continuously or periodically adjusted,when necessary, to align itself with the light beam. In addition tomoving the droplet 502 to realign the microlens with the light beam 511,the droplet 502 may also be moved when it is desired to steer the focusof the light beam 511 to a different focal point. One skilled in the artwill recognize that there are numerous causes for the droplet to movefrom its initial position to a different position. Whatever the reasonfor the droplet 502 being moved, the result is that the droplet 502 maybe moved during operations such that it is in a different position, suchas the position of the droplet represented by dashed line 514, comparedto its nominal, calibrated position.

Layer 515 of electrodes is used to calibrate the lens (e.g., eitherafter operations has concluded or periodically during operations). Asused herein calibrating the microlens refers to the process of returningthe droplet to its nominal, calibrated position relative to theelectrodes in layer 515. This calibration is achieved by applying aconstant, equal voltage V_(c) to the electrodes in layer 515 via leads506, where V_(c)>V_(O) volts, while at the same time passing a constantvoltage, that is equal to the droplet voltage V_(O), over the electrodesin layer 505 in a way such that each of the electrodes in layer 505experience the same voltage as the other electrodes in that layer (e.g.,V₁=V₅=a constant voltage). As further explained below, the result isthat the droplet 514 will move in direction 513 to return to itsnominal, calibrated position.

FIG. 6 shows a top plan view of the microlens of FIG. 5 and shows anexemplary configuration of the two layers of electrodes useful inaccomplishing the aforementioned calibration function. The electrodes inthe lower layer 505 in FIG. 5 are represented in FIG. 6 by electrodes614 thru 621. The electrodes in the upper layer 515 in FIG. 5 arerepresented in FIG. 6 as electrodes 603 through 610. These latterelectrodes are disposed in a pattern such that the sum of theintersection lengths of the circumference of the microlens droplet ofliquid with the second plurality of electrodes 603 thru 610 changes (inthis example the sum decreases) as the distance from the center of thepattern of electrodes increases. In other words, when the droplet iscentered relative to the second, upper layer of electrodes 603 thru 610,and its diameter is increased (e.g., by applying a constant voltageacross the first, lower layer of electrodes), the sum of the length ofintersection of the circumference of the droplet, represented by dashedline 602, with the electrodes will decrease. For example, as electrode603 extends away from the well, its lateral width (as shown in FIG. 6)decreases, i.e., the electrode becomes narrower. As a result, as thediameter of the droplet increases, the circumference of the dropletoverlaps with a smaller portion of the electrode. One skilled in the artwill recognize that there are other equally advantageous configurationsof the first, lower layer of electrodes 614 through 621 and the second,upper layer of electrodes 603 through 610 that are intended to beencompassed by the present invention.

As previously discussed, during operations, the droplet of the microlens601, which is coupled to voltage V_(O) via well 612, may be repositionedto, for example, the position represented by dashed line 602 by applyingvarious voltages V₁ through V₈ to the electrodes 614 through 621 in thelower, first layer of electrodes. To calibrate the microlens such thatthe droplet is returned to its nominal position, the voltage acrosselectrodes 614 through 621 is made constant such thatV₁=V₂=V₃=V₄=V₅=V₆=V₇=V₈=V_(O). By applying a voltage V_(c) to each ofelectrodes 603 through 610, where V_(c)>V_(O) volts, a driving force iscreated which will move the droplet 602 in direction 613 to a nominal,centered position relative to electrodes 603 through 610. The drivingforce needed to move the droplet in direction 613 is directlyproportional to the voltage square (V_(c))²across each electrodemultiplied by the intersection L_(n) between the outer circumference ofthe droplet and each of the electrodes 603 through 610. The upperelectrodes are disposed, for example, in a star-like pattern withwedge-like gaps between the electrodes (or other equally advantageousconfiguration) in a way such that the length of the intersection of thecircumference of the droplet and a particular electrode will decrease asthe droplet moves in the direction of that particular electrode. As aresult, the driving force will decrease as the droplet 602 moves indirection 613. The droplet 602 will move in direction 613 until(V_(c)*)²L₃=(V_(c)*)²L₄=(V_(c)*)²L₅=(V_(c)*)²L₆=(V_(c)*)²L₇=(V_(c)*)²L₈=(V_(c)*)²L₉=(V_(c)*)²L₁₀.For a constant V_(c) across all electrodes 603 through 610, thisrelationship can be simplified such that the droplet will move untilL₃=L₄=L₅=L₆=L₇=L₈=L₉=L₁₀. In other words, the droplet 602 will moveuntil the continuous reduction in the driving force due to the decreasein the length of contact between the circumference of the droplet 602and the individual electrodes 603 through 610 results in the equilibriumof the forces acting on the droplet. The size and number of thewedge-like gaps between the electrodes 603 through 610 is designed insuch a way as to insure that the motion of the droplet 602 halts at thepoint where it is in its nominal position, in this case centeredrelative to electrodes 603 through 610. By varying the value of thevoltage V_(c) one can achive a predetermined value of the microlenscontact angle and thus a predetermined focal length.

The foregoing merely illustrates the principles of the invention. Itwill thus be appreciated that those skilled in the art will be able todevise various arrangements which, although not explicitly described orshown herein, embody the principles of the invention and are within itsspirit and scope. Furthermore, all examples and conditional languagerecited herein are intended expressly to be only for pedagogicalpurposes to aid the reader in understanding the principles of theinvention and are to be construed as being without limitation to suchspecifically recited examples and conditions. Moreover, all statementsherein reciting aspects and embodiments of the invention, as well asspecific examples thereof, are intended to encompass functionalequivalents thereof.

1. A tunable liquid microlens comprising: a first plurality ofelectrodes; a conducting liquid; and a second plurality of electrodesconfigured such that application of an equal and constant voltage tosaid second plurality of electrodes causes said conducting liquid to bepositioned in a nominal position relative to the electrodes in eithersaid first plurality or said second plurality of electrodes.
 2. Thetunable liquid microlens of claim 1 further comprising a transparentconducting substrate of a material that is transparent to at least onewavelength of light.
 3. The tunable liquid microlens of claim 2 furthercomprising a dielectric insulating layer that insulates said pluralityof electrodes from said droplet.
 4. The tunable liquid microlens ofclaim 1 wherein a voltage across said conducting liquid is constant. 5.The tunable liquid microlens of claim 1 wherein the sum of theintersection lengths formed by an intersection of the circumference of adroplet of said conducting liquid with second plurality of electrodeschanges as the distance from the center of said second plurality ofelectrodes increases.
 6. A method for use in calibrating a liquidmicrolens with a droplet of conducting liquid, said method comprising:passing a first constant voltage over a first plurality of electrodes;and passing at least a second constant voltage over a second pluralityof electrodes in order to cause said droplet to move to a nominalposition.
 7. The method of claim 6 wherein the voltage passed over eachelectrode in said second plurality of electrodes is the same.
 8. Themethod of claim 6 wherein the voltage passed over each electrode in saidsecond plurality of electrodes is not the same.
 9. The method of 6wherein said second constant voltage is greater than a voltage on saiddroplet of conducting liquid.
 10. A tunable liquid microlens comprising:a first plurality of electrodes; a droplet of conducting liquid disposedon a hydrophobic surface; a second plurality of electrodes arranged in apattern and disposed between said first layer of electrodes and saiddroplet; and an insulating layer separating said droplet of conductingliquid from said first plurality of electrodes and said second pluralityof electrodes; wherein the sum of the intersection lengths formed by theintersection of the circumference of the droplet of liquid and thepattern of the second plurality of electrodes changes as the distancefrom the center of said pattern of said second plurality of electrodesincreases.
 11. The tunable liquid microlens of claim 10 wherein saidsecond plurality of electrodes is arranged in a star-like pattern.